Are random pure states useful for quantum computation?

TL;DR

This paper demonstrates that random pure states offer negligible quantum computational advantage over classical randomness, with their usefulness limited to classical probabilistic computation, unlike structured states like cluster states.

Contribution

It proves that random pure states do not enhance quantum computational power beyond classical probabilistic computation, extending results to less entangled states.

Findings

Random pure states do not increase computational power beyond BPP.

Random states are as useful as random bits for sampling tasks.

Results extend to states with less entanglement.

Abstract

We show the following: a randomly chosen pure state as a resource for measurement-based quantum computation, is - with overwhelming probability - of no greater help to a polynomially bounded classical control computer, than a string of random bits. Thus, unlike the familiar "cluster states", the computing power of a classical control device is not increased from P to BQP, but only to BPP. The same holds if the task is to sample from a distribution rather than to perform a bounded-error computation. Furthermore, we show that our results can be extended to states with significantly less entanglement than random states.